I did consider something like that. However I felt it might make things too complicated. Also I don't intend for this to have to permanently be in the living room. Only when we have children around that run a risk of accidentally touching the hot stove. But it would certainly be an option.

It's actually not bad. With it in place the door can still open enough to feed new wood in.When starting out I can pull it forward perhaps 15cm which is enough for the door to fully swing open. Obviously it is a barrier, that's kind of the point. But I've not found it to be a problem.